{"id":6224,"date":"2024-01-28T23:59:37","date_gmt":"2024-01-28T14:59:37","guid":{"rendered":"https:\/\/now0930.pe.kr\/wordpress\/?p=6224"},"modified":"2026-10-04T08:52:32","modified_gmt":"2026-10-03T23:52:32","slug":"109%ed%9a%8c-%ec%95%88%ec%a0%95%eb%8f%84-%ed%8c%90%eb%b3%84","status":"publish","type":"post","link":"https:\/\/now0930.pe.kr\/wordpress\/109%ed%9a%8c-%ec%95%88%ec%a0%95%eb%8f%84-%ed%8c%90%eb%b3%84\/","title":{"rendered":"109\ud68c \uc548\uc815\ub3c4 \ud310\ubcc4"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"933\" height=\"225\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-59.png\" alt=\"\" class=\"wp-image-6225\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-59.png 933w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-59-768x185.png 768w\" sizes=\"auto, (max-width: 933px) 100vw, 933px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-60.png\" alt=\"\" class=\"wp-image-6228\" style=\"width:610px;height:auto\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-60.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-60-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"936\" height=\"1280\" src=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-61.png\" alt=\"\" class=\"wp-image-6229\" srcset=\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-61.png 936w, https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/image-61-768x1050.png 768w\" sizes=\"auto, (max-width: 936px) 100vw, 936px\" \/><\/figure>\n\n\n\n<pre class=\"wp-block-code\"><code><iframe src =\"https:\/\/now0930.pe.kr\/wordpress\/wp-content\/uploads\/2024\/01\/109_Stability_critetion.html\" width = 600 height = 800 align = \"middle\"><\/iframe><\/code><\/pre>\n\n\n\n&#8220;`html\n<div class=\"chapter19-wide\">\n\n  <h1>109\ud68c \uc548\uc815\ub3c4 \ud310\ubcc4<\/h1>\n\n  <div class=\"subtitle\">\n    Routh-Hurwitz \u00b7 Root Locus \u00b7 Nyquist Plot\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>1. \ubb38\uc81c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \ub2e4\uc74c \ud3d0\ub8e8\ud504 \uc2dc\uc2a4\ud15c\uc774 \uc548\uc815\ud558\uae30 \uc704\ud55c\n      \uc81c\uc5b4\uc774\ub4dd K\uc758 \uc870\uac74\uc744\n      Nyquist \ud310\ubcc4\ubc95, Routh-Hurwitz,\n      \uadfc\uada4\uc801 \uc120\ub3c4\ub97c \uc774\uc6a9\ud558\uc5ec \uac01\uac01 \uad6c\ud55c\ub2e4.\n    <\/p>\n\n    <pre>\n                 +             K\n      R(s) ---->(\u03a3)---->[ ------------- ]-----> C(s)\n                 - ^       s(s+1)(2s+1)           |\n                   |                               |\n                   +-------------------------------+\n                        Unity Feedback\n    <\/pre>\n\n    <div class=\"formula\">\n      G(s)\n      =\n      K\n      \/\n      [s(s+1)(2s+1)]\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>2. Routh-Hurwitz \u2014 \ud2b9\uc131\ubc29\uc815\uc2dd<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Unity Feedback\uc5d0\uc11c \ud2b9\uc131\ubc29\uc815\uc2dd\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      1 + G(s) = 0\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      1\n      +\n      K\/[s(s+1)(2s+1)]\n      =\n      0\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      s(s+1)(2s+1)+K=0\n    <\/div>\n\n    <p>\n      \uc804\uac1c\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      2s<sup>3<\/sup>\n      +\n      3s<sup>2<\/sup>\n      +\n      s\n      +\n      K\n      =\n      0\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>3. Routh Array<\/h2>\n\n  <div class=\"card\">\n\n    <pre>\n      s\u00b3 |     2          1\n      s\u00b2 |     3          K\n      s\u00b9 |  (3-2K)\/3      0\n      s\u2070 |     K\n    <\/pre>\n\n    <p>\n      \uc548\uc815\ud558\uae30 \uc704\ud574\uc11c\ub294\n      Routh Array \uccab \ubc88\uc9f8 \uc5f4\uc758 \ubaa8\ub4e0 \ud56d\uc774\n      \uac19\uc740 \ubd80\ud638\ub97c \uac00\uc838\uc57c \ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      2 &gt; 0\n    <\/div>\n\n    <div class=\"formula\">\n      3 &gt; 0\n    <\/div>\n\n    <div class=\"formula\">\n      (3-2K)\/3 &gt; 0\n    <\/div>\n\n    <div class=\"formula\">\n      K &gt; 0\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      3 &#8211; 2K &gt; 0\n    <\/div>\n\n    <div class=\"formula\">\n      K &lt; 3\/2\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        Routh-Hurwitz \uc548\uc815\uc870\uac74\n        <br><br>\n        0 &lt; K &lt; 3\/2\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>4. Root Locus \u2014 \ud5c8\uc218\ucd95 \ud1b5\uacfc \uc870\uac74<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Root Locus\uac00 \ud5c8\uc218\ucd95\uc744 \ud1b5\uacfc\ud558\ub294\n      \uc548\uc815 \ud55c\uacc4\ub97c \uad6c\ud558\uae30 \uc704\ud574\n    <\/p>\n\n    <div class=\"formula\">\n      s = j\u03c9\n    <\/div>\n\n    <p>\n      \ub97c \ud2b9\uc131\ubc29\uc815\uc2dd\uc5d0 \ub300\uc785\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      2(j\u03c9)<sup>3<\/sup>\n      +\n      3(j\u03c9)<sup>2<\/sup>\n      +\n      j\u03c9\n      +\n      K\n      =\n      0\n    <\/div>\n\n    <p>\n      \uc2e4\uc218\ubd80\uc640 \ud5c8\uc218\ubd80\ub85c \ubd84\ub9ac\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      K &#8211; 3\u03c9<sup>2<\/sup>\n      +\n      j(\u03c9-2\u03c9<sup>3<\/sup>)\n      =\n      0\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>5. \ud5c8\uc218\ubd80 \uc870\uac74<\/h2>\n\n  <div class=\"card\">\n\n    <div class=\"formula\">\n      \u03c9 &#8211; 2\u03c9<sup>3<\/sup>\n      =\n      0\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9(1-2\u03c9<sup>2<\/sup>)\n      =\n      0\n    <\/div>\n\n    <p>\n      \u03c9\u22600\uc778 \ud5c8\uc218\ucd95 \uad50\uc810\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      1 &#8211; 2\u03c9<sup>2<\/sup>\n      =\n      0\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9<sup>2<\/sup>\n      =\n      1\/2\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9\n      =\n      1\/\u221a2\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c Root Locus\ub294 \uc548\uc815 \ud55c\uacc4\uc5d0\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      s\n      =\n      \u00b1j\/\u221a2\n    <\/div>\n\n    <p>\n      \ub97c \ud1b5\uacfc\ud55c\ub2e4.\n    <\/p>\n\n    <pre>\n                Im\n                \u2191\n\n                \u25cf  +j\/\u221a2\n                |\n    ------------+--------------------------\u2192 Re\n                |\n                \u25cf  -j\/\u221a2\n\n              \uc548\uc815 \ud55c\uacc4\n    <\/pre>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>6. Root Locus \u2014 \uc784\uacc4 Gain<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc2e4\uc218\ubd80 \uc870\uac74\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      K &#8211; 3\u03c9<sup>2<\/sup>\n      =\n      0\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      K\n      =\n      3\u03c9<sup>2<\/sup>\n    <\/div>\n\n    <p>\n      \u03c9\u00b2=1\/2\ub97c \ub300\uc785\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      K\n      =\n      3\/2\n    <\/div>\n\n    <div class=\"memory\">\n      <strong>\n        K = 3\/2\uc5d0\uc11c \ud3d0\ub8e8\ud504 pole\uc774\n        \ud5c8\uc218\ucd95 s=\u00b1j\/\u221a2\uc5d0 \uc704\uce58\ud55c\ub2e4.\n        <br><br>\n        \ub530\ub77c\uc11c \uc548\uc815\uc601\uc5ed\uc740\n        0 &lt; K &lt; 3\/2\uc774\ub2e4.\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>7. Nyquist Plot<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Open-Loop Transfer Function\uc740\n    <\/p>\n\n    <div class=\"formula\">\n      L(s)\n      =\n      K\n      \/\n      [s(s+1)(2s+1)]\n    <\/div>\n\n    <p>\n      \uc774\ub2e4.\n    <\/p>\n\n    <p>\n      \uc8fc\ud30c\uc218\uc751\ub2f5\uc744 \uad6c\ud558\uae30 \uc704\ud574\n    <\/p>\n\n    <div class=\"formula\">\n      s = j\u03c9\n    <\/div>\n\n    <p>\n      \ub97c \ub300\uc785\ud55c\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      L(j\u03c9)\n      =\n      K\n      \/\n      [\n      j\u03c9(j\u03c9+1)(2j\u03c9+1)\n      ]\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>8. Nyquist \uc2dd \uc804\uac1c<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uba3c\uc800\n    <\/p>\n\n    <div class=\"formula\">\n      (1+j\u03c9)(1+2j\u03c9)\n      =\n      1\n      &#8211;\n      2\u03c9<sup>2<\/sup>\n      +\n      j3\u03c9\n    <\/div>\n\n    <p>\n      \uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      j\u03c9(1+j\u03c9)(1+2j\u03c9)\n    <\/div>\n\n    <div class=\"formula\">\n      =\n      -3\u03c9<sup>2<\/sup>\n      +\n      j\u03c9(1-2\u03c9<sup>2<\/sup>)\n    <\/div>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      L(j\u03c9)\n      =\n      K\n      \/\n      [\n      -3\u03c9<sup>2<\/sup>\n      +\n      j\u03c9(1-2\u03c9<sup>2<\/sup>)\n      ]\n    <\/div>\n\n    <p>\n      \ucf24\ub808\ubcf5\uc18c\uc218\ub97c \uacf1\ud558\uba74\n    <\/p>\n\n    <div class=\"formula\">\n      L(j\u03c9)\n      =\n      [\n      -3K\u03c9<sup>2<\/sup>\n      &#8211;\n      jK\u03c9(1-2\u03c9<sup>2<\/sup>)\n      ]\n      \/\n      [\n      9\u03c9<sup>4<\/sup>\n      +\n      \u03c9<sup>2<\/sup>(1-2\u03c9<sup>2<\/sup>)<sup>2<\/sup>\n      ]\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>9. \uc74c\uc758 \uc2e4\uc218\ucd95 \uad50\uc810<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      Nyquist Plot\uc774 \uc2e4\uc218\ucd95\uc744 \uc9c0\ub098\ub294 \uc870\uac74\uc740\n      \ud5c8\uc218\ubd80\uac00 0\uc774 \ub418\ub294 \uac83\uc774\ub2e4.\n    <\/p>\n\n    <div class=\"formula\">\n      \u03c9(1-2\u03c9<sup>2<\/sup>)\n      =\n      0\n    <\/div>\n\n    <p>\n      \u03c9\u22600\uc5d0\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      \u03c9<sup>2<\/sup>\n      =\n      1\/2\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9\n      =\n      1\/\u221a2\n    <\/div>\n\n    <p>\n      \uc774\ub54c\n    <\/p>\n\n    <div class=\"formula\">\n      L(j\u03c9)\n      =\n      K\/(-3\u03c9<sup>2<\/sup>)\n    <\/div>\n\n    <p>\n      \u03c9\u00b2=1\/2\uc774\ubbc0\ub85c\n    <\/p>\n\n    <div class=\"formula\">\n      L(j\u03c9)\n      =\n      -2K\/3\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>10. Nyquist \uc784\uacc4 Gain<\/h2>\n\n  <div class=\"card\">\n\n    <p>\n      \uc548\uc815 \ud55c\uacc4\uc5d0\uc11c\ub294 Nyquist Plot\uc774\n      Critical Point\n    <\/p>\n\n    <div class=\"formula\">\n      -1 + j0\n    <\/div>\n\n    <p>\n      \uc744 \uc9c0\ub09c\ub2e4.\n    <\/p>\n\n    <p>\n      \ub530\ub77c\uc11c\n    <\/p>\n\n    <div class=\"formula\">\n      -2K\/3\n      =\n      -1\n    <\/div>\n\n    <div class=\"formula\">\n      K\n      =\n      3\/2\n    <\/div>\n\n    <pre>\n                  Im\n                  \u2191\n                  |\n                  |\n       -1 \u25cf-------\u25cf----------------------\u2192 Re\n          Critical -2K\/3\n           Point\n\n       K &lt; 3\/2  \u2192 \uad50\uc810\uc774 -1\uc758 \uc624\ub978\ucabd\n       K = 3\/2  \u2192 \uad50\uc810\uc774 -1\n       K &gt; 3\/2  \u2192 \uad50\uc810\uc774 -1\uc758 \uc67c\ucabd\n    <\/pre>\n\n    <div class=\"memory\">\n      <strong>\n        Nyquist \uc548\uc815 \ud55c\uacc4\n        <br><br>\n        K = 3\/2\n        <br><br>\n        \uc548\uc815\uc870\uac74:\n        0 &lt; K &lt; 3\/2\n      <\/strong>\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>11. \uc138 \ubc29\ubc95\uc758 \uacb0\uacfc<\/h2>\n\n  <div class=\"table-wrap\">\n\n    <table>\n\n      <thead>\n        <tr>\n          <th>\ud310\ubcc4 \ubc29\ubc95<\/th>\n          <th>\uacc4\uc0b0 \uae30\uc900<\/th>\n          <th>\uc784\uacc4\uac12<\/th>\n          <th>\uc548\uc815\uc870\uac74<\/th>\n        <\/tr>\n      <\/thead>\n\n      <tbody>\n\n        <tr>\n          <td><strong>Routh-Hurwitz<\/strong><\/td>\n          <td>\n            (3-2K)\/3 &gt; 0\n          <\/td>\n          <td>\n            K = 3\/2\n          <\/td>\n          <td>\n            0 &lt; K &lt; 3\/2\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Root Locus<\/strong><\/td>\n          <td>\n            s = \u00b1j\/\u221a2\n          <\/td>\n          <td>\n            K = 3\/2\n          <\/td>\n          <td>\n            0 &lt; K &lt; 3\/2\n          <\/td>\n        <\/tr>\n\n        <tr>\n          <td><strong>Nyquist<\/strong><\/td>\n          <td>\n            L(j\u03c9)=-1\n          <\/td>\n          <td>\n            K = 3\/2\n          <\/td>\n          <td>\n            0 &lt; K &lt; 3\/2\n          <\/td>\n        <\/tr>\n\n      <\/tbody>\n\n    <\/table>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <h2>12. \uc774\ubbf8\uc9c0 \ud575\uc2ec \uacb0\uacfc<\/h2>\n\n  <div class=\"memory\">\n\n    <div class=\"formula\">\n      Characteristic Equation\n      =\n      2s<sup>3<\/sup>\n      +\n      3s<sup>2<\/sup>\n      +\n      s\n      +\n      K\n    <\/div>\n\n    <div class=\"formula\">\n      \u03c9\n      =\n      1\/\u221a2\n    <\/div>\n\n    <div class=\"formula\">\n      K<sub>critical<\/sub>\n      =\n      3\/2\n    <\/div>\n\n    <div class=\"formula\">\n      0\n      &lt;\n      K\n      &lt;\n      3\/2\n    <\/div>\n\n  <\/div>\n\n\n  <!-- ================================================= -->\n  <div class=\"keywords\">\n    Stability, Routh-Hurwitz, Root Locus,\n    Nyquist Plot, Critical Gain,\n    Imaginary Axis Crossing, Characteristic Equation\n  <\/div>\n\n<\/div>\n&#8220;`\n","protected":false},"excerpt":{"rendered":"<p>&#8220;`html 109\ud68c \uc548\uc815\ub3c4 \ud310\ubcc4 Routh-Hurwitz \u00b7 Root Locus \u00b7 Nyquist Plot 1. \ubb38\uc81c \ub2e4\uc74c \ud3d0\ub8e8\ud504 \uc2dc\uc2a4\ud15c\uc774 \uc548\uc815\ud558\uae30 \uc704\ud55c \uc81c\uc5b4\uc774\ub4dd K\uc758 \uc870\uac74\uc744 Nyquist \ud310\ubcc4\ubc95, Routh-Hurwitz, \uadfc\uada4\uc801 \uc120\ub3c4\ub97c \uc774\uc6a9\ud558\uc5ec \uac01\uac01 \uad6c\ud55c\ub2e4. + K R(s) &#8212;->(\u03a3)&#8212;->[ &#8212;&#8212;&#8212;&#8212;- ]&#8212;&#8211;> C(s) &#8211; ^ s(s+1)(2s+1) | | | +&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;&#8212;-+ Unity Feedback G(s) = K \/ [s(s+1)(2s+1)] 2. Routh-Hurwitz \u2014 \ud2b9\uc131\ubc29\uc815\uc2dd Unity [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[1185],"tags":[1223,1239,1233],"class_list":["post-6224","post","type-post","status-publish","format-standard","hentry","category-1185","tag-nyquistplot","tag-root-locus","tag-routh-hurwitz"],"jetpack_sharing_enabled":true,"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6224","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/comments?post=6224"}],"version-history":[{"count":4,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6224\/revisions"}],"predecessor-version":[{"id":9559,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/posts\/6224\/revisions\/9559"}],"wp:attachment":[{"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/media?parent=6224"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/categories?post=6224"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/now0930.pe.kr\/wordpress\/wp-json\/wp\/v2\/tags?post=6224"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}